View source for Lattice system

<font color="blue">Système réticulaire</font> (''Fr''). <font color="red">Gittersystem</font> (''Ge''). <font color="black">Sistema reticolare</font> (''It''). <font color="purple">格子系</font> (''Ja'').
== Definition ==

A '''lattice system''' of space groups contains complete [[Bravais class]]es. All those Bravais classes which intersect exactly the same set of [[geometric crystal class]]es belong to the same lattice system.

== Alternative definition ==

A '''lattice system''' of space groups contains complete [[Bravais class]]es. All those Bravais classes belong to the same lattice system for which the [[Bravais arithmetic class]]es belong to the same (holohedral) [[geometric crystal class]].

== Lattice systems in two and three dimensions ==
In two-dimensional space there exist four lattice systems:
* oblique
* rectangular
* square
* hexagonal

In three-dimensional space there exist seven lattice systems:
* triclinic
* monoclinic
* orthorhombic
* tetragonal
* rhombohedral
* hexagonal
* cubic

Note that the adjective ''trigonal'' refers to a [[crystal system]], not to a lattice system. Rhombohedral crystals belong to the trigonal [[crystal system]], but trigonal crystals may belong to the rhombohedral or to the hexagonal lattice system.

== Note ==
In earlier editions of ''International Tables for Crystallography, Volume A & Volume E'', the lattice systems were called ''Bravais-flock systems'' or ''Bravais systems''.

== See also ==
*[[Bravais class]]
*Chapter 1.3.4.4.2 of ''International Tables for Crystallography, Volume A'', 6th edition

[[category: Fundamental crystallography]]